5 papers
Poincaré index and the volume functional of unit vector fields on punctured spheres
Fabiano G. B. Brito, André O. Gomes, Icaro Gonçalves
For , we exhibit a lower bound for the volume of a unit vector field on depending on the absolute values of its Poincaré indices aro…
A topological lower bound for the energy of a unit vector field on a closed hypersurface of the euclidean space. The 3-dimensional case
Fabiano G. B. Brito, Andre O. Gomes, Adriana V. Nicoli
In this short note we prove that the degree of the Gauss map ν of a closed 3-dimensional hypersurface of the Euclidean space is a lower bound for the total bending functional B, in…
A theorem about vector fields with the "proportional volume property"
Fabiano Brito, André Gomes, Robson Mesquita
In this paper, we define a certain "proportional volume property" for an unit vector field on a spherical domain in S3. We prove that the volume of these vector fields has an absol…
Energy of solenoidal vector fields on spherical domains
Fabiano Brito, André Gomes
We present a boundary version of a theorem about solenoidal unit vector fields with minimum energy on a spherical domain of an odd dimensional Euclidean sphere.
Energy and volume of vector fields on spherical domains
Fabiano G. B. Brito, André Gomes, Giovanni S. Nunes
We present in this paper a \boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of threedimensional Euclidean sphere.